Consider the following glossary Sx x x is scary Fx x x is a

Consider the following glossary:

Sx: {x: x is scary}

Fx: {x: x is a film}

Rx: {x: x is romantic}

Ax: {x: x is afraid}

a = Alex

b = Alyssa

Using this glossary, select the best translation of the following english sentences into MPL:

1.1. Every scary film is not romantic.

[1] ¬x((Sx F x) ¬Rx)

[2] x((Sx F x) ¬Rx)

[3] x((Rx F x) Sx)

[4] ¬x((¬Sx F x) Rx)

1.2. Every romantic film is scary.

[1] ¬x((Sx F x) Rx)

[2] x((Sx F x) Rx)

[3] ¬x((Sx ¬F x) Rx)

[4] x((Rx F x) Sx)

1.3. Either Alex is scary, or he is romantic and he is unafraid.

[1] (Sa (Ra ¬Aa))

[2] (Sa (Rb Aa))

[3] (¬Sa (Ra Aa))

[4] (Sb (Ra Aa))

1.4. Not every unromantic film is scary.

[1] ¬x((Rx ¬Sx) F x)

[2] x(Rx (Sx F x))

[3] ¬x((F x ¬Rx) Sx)

[4] ¬x((F x Rx) ¬Sx)

1.5. If Alex is afraid if and only if Alyssa is scary, then Alex is unafraid.

[1] (Aa (Sb Aa))

[2] ((Aa Sb) ¬Aa)

[3] ((Aa Sb) Aa)

[4] ((Aa Sb) Aa)

1.6. If Alex is romantic just in case some film is scary, then Alex is not romantic.

[1] ((Ra x(F x Sx)) ¬Ra)

[2] (Ra x((F x Sx) Rx))

[3] (Ra x((F x Sx) ¬Rx))

[4] ((Ra x((F x Sx)) ¬Rx))

1.7. Alex is not romantic and Alyssa is scary, only if Alyssa being scary is sufficient for Alex to not be romantic.

[1] ((¬Ra (Sb ¬Ra)) Sb)

[2] ((¬Ra Sb) (Sb ¬Ra))

[3] ((¬Ra (Ra ¬Sb)) Sb)

[4] ((¬Ra Ra) ¬Sb) Sb)

1.8. If every film is not scary, then Alex is afraid only if Alyssa is unafraid.

[1] (x(F x ¬Sx) (Aa ¬Ab))

[2] x(F x (¬Sx (Aa Ab)))

[3] ((Aa Ab) x(F x ¬Sx))

[4] x(F x (¬Sx (Aa Ab)))

1.9. If every scary film is romantic unless it isn’t, then no scary film is romantic.

[1] (x((Sx F x) (¬Rx Rx)) ¬x(Sx (Rx F x)))

[2] (x((Sx F x) (Rx Rx)) ¬x(Sx (Rx F x)))

[3] (x((Sx F x) (Rx Rx)) ¬x(Sx (Rx F x)))

[4] (x((Sx F x) (¬Rx ¬Rx)) ¬x(Sx (Rx F x))))

1.10. Alex is not romantic but Alyssa is unless Alex is scary.

[1] (¬Ra (Sa Rb))

[2] (¬Ra (¬Rb ¬Sa))

[3] (¬Ra (Rb Sa))

[4] (¬Ra (¬Rb Sa))

Solution

1.1. Every scary film is not romantic.

Ans : [2] x((Sx F x) ¬Rx)

1.2. Every romantic film is scary.

Ans: [4] x((Rx F x) Sx)

1.3. Either Alex is scary, or he is romantic and he is unafraid.

Ans: [1] (Sa (Ra ¬Aa))

1.4. Not every unromantic film is scary.

Ans: [3] ¬x((F x ¬Rx) Sx)